a. Let a and b be constants and let yi = axi +b for . What are the relationships between x ¯and y¯ and between sx2and sy2? b. A sample of temperatures for initiating a certain chemical reaction yielded a sample average (°C) of 87.3 and a sample standard deviation of 1.04. What are the sample average and standard deviation measured in °F? [Hint: 9/5C+ 32 .]

Answer: Step1: a). Let ‘a’ and ‘b’ be constants. And let y = ax +b. i i Now we have to find the relationships between x and y and between s and s . x y So that, yi y = n (ai +b) = n a xi+ b = n a x + nb i = n a xi nb = n + n y = a x + b Then, 2 (yi y) s = y n 1 2 (axi+b (ax+b)) = n 1 (ax ax) i = n 1 a2(xix)2 = n1 2 (i x) sy= a s2 2x ( here, s x ) n 1 Step2: b). Given, a sample of temperatures for initiating a certain chemical reaction yielded a sample average (°C) of 87.3 and a sample standard deviation of 1.04. We have to find the sample average and standard deviation measured in °F. Let x = °C , y = °F. Sample average y = 5 + 32 = (87.3) + 32 5 y = 189.14 °F Therefore, sample average y = 189.14 °F . Sample standard deviation 2 sy= sy 9 2 2 = (5) (1.04) = 3.5044 = 1.872 °F sy= 1.872 °F Therefore, sample standard deviation y = 1.872 °F .